According to reports on Goal.com, Zamora and Fulham boss Martin Jol's relationship is deteriorating.
The pair are believed to have had a number of disagreements over Jol's decision to rest the England international for Fulham's Europa League games.
“Jol has a poor relationship with Zamora and it is no secret that they do not see eye to eye,” a source said.
“Fulham could be willing to listen to offers for him but it depends on what happens with the other forwards and where they are in the table in January.
“If Fulham are struggling with around 16 points, they are more likely to trust in the players who have helped keep them up quite comfortably in the last three seasons.
"If they have around 22-26 points, there could be some high-profile changes and you will see a gradual break-up of what is an ageing squad.”
West Ham seem to be leading the chase for Zamora, as the player wants to stay in London and the surrounding area, however fellow promotion chasers Crystal Palce and Brighton are also keeping tabs on the 30-year-old's situation.
Zamora has two-and-a-half years remaining on his current deal with Fulham and the club value him at £5million.